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Time Complexity of Population-Based Metaheuristics

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Mendel

Mendel 2023年第2期29卷 255-260页

作者： Omran, Mahamed G. H. Engelbrecht, Andries Computer Science Department Gulf University for Science & Technology Kuwait Department of Industrial Engineering and Computer Science Division Stellenbosch University South Africa Centre for Applied Mathematics and Bioinformatics Gulf University for Science & Technology Kuwait

This paper is a brief guide aimed at evaluating the time complexity of metaheuristic algorithms both mathematically and empirically. Starting with the mathematical foundational principles of time complexity analysis, key notations and fundamen-tal concepts necessary for computing the time efficiency of a metaheuristic are introduced. The paper then applies these principles on three well-known meta-heuristics, i.e. differential evolution, harmony search and the firefly algorithm. A procedure for the empirical analysis of metaheuristics’ time efficiency is then presented. The procedure is then used to empirically analyze the computational cost of the three aforementioned metaheuristics. The pros and cons of the two approaches, i.e. mathematical and empirical analysis, are discussed. © 2023, Brno University of Technology. All rights reserved.

关键词： Optimization

Multilevel Particle Filters for a Class of Partially Observed Piecewise Deterministic Markov Processes

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arXiv 2023年

作者： Jasra, Ajay Kamatani, Kengo Maama, Mohamed Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Institute of Statistical Mathematics Tokyo190-0014 Japan

In this paper we consider the filtering of a class of partially observed piecewise deterministic Markov processes (PDMPs). In particular, we assume that an ordinary differential equation (ODE) drives the deterministic element and can only be solved numerically via a time discretization. We develop, based upon the approach in [20], a new particle and multilevel particle filter (MLPF) in order to approximate the filter associated to the discretized ODE. We provide a bound on the mean square error associated to the MLPF which provides guidance on setting the simulation parameter of that algorithm and implies that significant computational gains can be obtained versus using a particle filter. Our theoretical claims are confirmed in several numerical examples. Copyright © 2023, The Authors. All rights reserved.

关键词： Ordinary differential equations

A Pseudo-Spectral Scheme for Systems of Two-Point Boundary Value Problems with Left and Right Sided Fractional Derivatives and Related Integral Equations

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computer Modeling in Engineering & sciences 2021年第7期128卷 21-41页

作者： I.G.Ameen N.A.Elkot M.A.Zaky A.S.Hendy E.H.Doha Department of Mathematics Faculty of ScienceAl-Azhar UniversityCairoEgypt Department of Mathematics Faculty of ScienceCairo UniversityGiza12613Egypt Department of Applied Mathematics Physics DivisionNational Research CentreDokkiCairo12622Egypt Department of Computational Mathematics and Computer Science Institute of Natural Sciences and MathematicsUral Federal UniversityYekaterinburg620002Russia Department of Mathematics Faculty of ScienceBenha UniversityBenha13511Egypt

We target here to solve numerically a class of nonlinear fractional two-point boundary value problems involving left-and right-sided fractional *** main ingredient of the proposed method is to recast the problem into an equivalent system of weakly singular integral ***,a Legendre-based spectral collocation method is developed for solving the transformed ***,we can make good use of the advantages of the Gauss quadrature *** present the construction and analysis of the collocation *** results can be indirectly applied to solve fractional optimal control problems by considering the corresponding Euler–Lagrange *** numerical examples are given to confirm the convergence analysis and robustness of the scheme.

关键词： Spectral collocation method weakly singular integral equations two-point boundary value problems convergence analysis

Unbiased Parameter Estimation for Bayesian Inverse Problems

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arXiv 2025年

作者： Chada, Neil K. Jasra, Ajay Maama, Mohamed Tempone, Raul Department of Mathematics City University of Hong Kong China School of Data Science The Chinese University of Hong Kong Shenzhen CN Shenzhen China Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a solution of a differential equation and, even if exact solutions are available, an analytical intractability of the marginal likelihood and its associated gradient, which is used for parameter estimation. The focus of this article is to deliver unbiased estimates of the unknown parameters, that is, stochastic estimators that, in expectation, are equal to the maximizer of the marginal likelihood, and possess no numerical approximation error. Based upon the ideas of [4] we develop a new approach for unbiased parameter estimation for Bayesian inverse problems. We prove unbiasedness and establish numerically that the associated estimation procedure is faster than the current state-of-the-art methodology for this problem. We demonstrate the performance of our methodology on a range of problems which include a PDE and ODE. Copyright © 2025, The Authors. All rights reserved.

关键词： Markov processes

An Improved Unbiased Particle Filter

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arXiv 2023年

作者： Jasra, Ajay Maama, Mohamed Ombao, Hernando Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Statistics Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

In this paper we consider the filtering of partially observed multi-dimensional diffusion processes that are observed regularly at discrete times. We assume that, for numerical reasons, one has to time-discretize the diffusion process which typically leads to filtering that is subject to discretization bias. The approach in [16] establishes that when only having access to the time discretized diffusion it is possible to remove the discretization bias with an estimator of finite variance. We improve on the method in [16] by introducing a modified estimator based on the recent work of [17]. We show that this new estimator is unbiased and has finite variance. Moreover, we conjecture and verify in numerical simulations that substantial gains are obtained. That is, for a given mean square error (MSE) and a particular class of multi-dimensional diffusion, the cost to achieve the said MSE falls. Copyright © 2023, The Authors. All rights reserved.

关键词： Mean square error

Prognostic Kalman Filter Based Bayesian Learning Model for Data Accuracy Prediction

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computers, Materials & Continua 2022年第7期72卷 243-259页

作者： S.Karthik Robin Singh Bhadoria Jeong Gon Lee Arun Kumar Sivaraman Sovan Samanta A.Balasundaram Brijesh Kumar Chaurasia S.Ashokkumar Department of ECE College of Engineering and TechnologySRM Institute of Science and TechnologyVadapalaniChennai600026India Department of CSE Birla Institute of Applied Sciences(BIAS)BhimtalUttarakhand263136India Division of Applied Mathematics Wonkwang University460Iksan-DaeroIksan-SiJeonbuk54538Korea School of Computer Science and Engineering Vellore Institute of Technology(VIT)Chennai600127India Department of Mathematics Tamralipta MahavidyalayaWest Bengal721636India School of Computer Science and Engineering Center for Cyber Physical SystemsVellore Institute of Technology(VIT)Chennai600127India Indian Institute of Information Technology(IIIT) LucknowUttar Pradesh226002India Department of Computer Science and Engineering Saveetha School of EngineeringSIMATSChennai602105India

Data is always a crucial issue of concern especially during its prediction and computation in digital *** paper exactly helps in providing efficient learning mechanism for accurate predictability and reducing redundant data *** also discusses the Bayesian analysis that finds the conditional probability of at least two parametric based predictions for the *** paper presents a method for improving the performance of Bayesian classification using the combination of Kalman Filter and *** method is applied on a small dataset just for establishing the fact that the proposed algorithm can reduce the time for computing the clusters from *** proposed Bayesian learning probabilistic model is used to check the statistical noise and other inaccuracies using unknown *** scenario is being implemented using efficient machine learning algorithm to perpetuate the Bayesian probabilistic *** also demonstrates the generative function forKalman-filer based prediction model and its *** paper implements the algorithm using open source platform of Python and efficiently integrates all different modules to piece of code via Common Platform Enumeration(CPE)for Python.

关键词： Bayesian learning model kalman filter machine learning data accuracy prediction

Applying Layer-Wise Relevance Propagation on U-Net Architectures 27th

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Applying Layer-Wise Relevance Propagation on U-Net Architect...

27th International Conference on Pattern Recognition, ICPR 2024

作者： Weinberger, Patrick Fröhler, Bernhard Heim, Anja Gall, Alexander Bodenhofer, Ulrich Senck, Sascha Research Group Computed Tomography University of Applied Sciences Upper Austria Wels Austria School of Informatics Communication and Media University of Applied Sciences Upper Austria Wels Austria Johannes Kepler University Linz Linz Austria Faculty of Computer Science and Mathematics University of Passau Passau Germany Division Development Center X-ray Technology Fraunhofer Institute for Integrated Circuits IIS Erlangen Germany

ISBN: (纸本)9783031781971

For safety critical applications, it is still a challenge to use AI and fulfill all regulatory requirements. Medicine/healthcare and transportation are two fields where regulatory requirements are of fundamental importance. A wrong decision can lead to serious hazards or even deaths. In these fields, semantic segmentation is often utilized to extract features. Especially U-Net architectures are used. This paper shows how to apply layer-wise relevance propagation (LRP) to a trained U-Net architecture. We achieve an efficient explanation of a segmentation by back-propagating the whole resulting image. To tackle the non-linear results of the LRP, we introduce a threshold mechanism in combination with a logarithmic transfer function to preprocess the data for visualization. We demonstrate our method on three use cases: the segmentation of a fiber-reinforced polymer in the field of non-destructive testing, the segmentation of pedestrians in an automotive application, and a lung segmentation example from the medical domain. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Semantic Segmentation

Developing, Analyzing, and Evaluating Vehicular Lane Keeping Algorithms Under Dynamic Lighting and Weather Conditions Using Electric Vehicles

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arXiv 2024年

作者： Khalfin, Michael Volgren, Jack Jones, Matthew LeGoullon, Luke Siegel, Joshua Chung, Chan-Jin Department of Computational Applied Mathematics Rice University United States Department of Computer Science and Engineering Pennsylvania State University United States Department of Mathematics and Computer Science Willamette University United States Division of Computer Science and Engineering Louisiana State University United States Department of Computer Science and Engineering Michigan State University United States Department of Mathematics and Computer Science Lawrence Technological University United States

Self-driving vehicles have the potential to reduce accidents and fatalities on the road. Many production vehicles already come equipped with basic self-driving capabilities, but have trouble following lanes in adverse lighting and weather conditions. Therefore, we develop, analyze, and evaluate two vehicular lane-keeping algorithms under dynamic weather conditions using a combined deep learning- and hand-crafted approach and an end-to-end deep learning approach. We use image segmentation- and linear-regression based deep learning to drive the vehicle toward the center of the lane, measuring the amount of laps completed, average speed, and average steering error per lap. Our hybrid model completes more laps than our end-to-end deep learning model. In the future, we are interested in combining our algorithms to form one cohesive approach to lane-following. © 2024, CC BY.

关键词： computer vision

Looking through the mind's eye via multimodal encoder-decoder networks

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arXiv 2024年

作者： Afrasiyabi, Arman Busch, Erica Singh, Rahul Bhaskar, Dhananjay Caplette, Laurent Turk-Browne, Nicholas Krishnaswamy, Smita Department of Computer Science Applied Mathematics Program Department of Psychology O Department of Genetics Wu Tsai Institute United States Yale University United States

In this work, we explore the decoding of mental imagery from subjects using their fMRI measurements. In order to achieve this decoding, we first created a mapping between a subject's fMRI signals elicited by the videos the subjects watched. This mapping associates the high dimensional fMRI activation states with visual imagery. Next, we prompted the subjects textually, primarily with emotion labels which had no direct reference to visual objects. Then to decode visual imagery that may have been in a person's mind's eye, we align a latent representation of these fMRI measurements with a corresponding video-fMRI based on textual labels given to the videos themselves. This alignment has the effect of overlapping the video fMRI embedding with the text-prompted fMRI embedding, thus allowing us to use our fMRI-to-video mapping to decode. Additionally, we enhance an existing fMRI dataset, initially consisting of data from five subjects, by including recordings from three more subjects gathered by our team. We demonstrate the efficacy of our model on this augmented dataset both in accurately creating a mapping, as well as in plausibly decoding mental imagery. © 2024, CC BY.

关键词： Mapping